A multivariate phylogenetic comparative method incorporating a flexible function between discrete and continuous traits
One major challenge of using the phylogenetic comparative method (PCM) is the analysis of the evolution of interrelated continuous and discrete traits in a single multivariate statistical framework. In addition, more intricate parameters such as branch-specific directional selection have rarely been integrated into such multivariate PCM frameworks. Here, originally motivated to analyze the complex evolutionary trajectories of group size (continuous variable) and social systems (discrete variable) in African subterranean rodents, we develop a flexible approach using approximate Bayesian computation (ABC). Specifically, our multivariate ABC-PCM method allows the user to flexibly model an underlying latent evolutionary function between continuous and discrete traits. The ABC-PCM also simultaneously incorporates complex evolutionary parameters such as branch-specific selection. This study highlights the flexibility of ABC-PCMs in analyzing the evolution of phenotypic traits interrelated in a complex manner.
KeywordsPhylogenetic comparative method (PCM) Approximate Bayesian computation (ABC) Multivariate analysis Social evolution African mole rats
We would like to thank Dustin R. Rubenstein, Rafael Maia, and Margaret E. O’Brien at Columbia University and Jessica Zung at Princeton University for useful comments and advice. Masahito Tsuboi at University of Oslo also provided useful insights on the earlier version of manuscript. Two reviewers gave detailed and helpful comments on the manuscript. This study was financially supported by MEXT (No. 25711025) to K. N.
YH and KN conceived, designed, and performed the analysis. Both discussed the result and wrote the final manuscript.
Compliance with ethical standards
Conflict of interest
Both authors declare that they have no conflict of interest.
- Beauchamp G (1999) The evolution of communal roosting in birds: origin and secondary losses. Behav Ecol 10:675–687Google Scholar
- Beaumont MA (2010) Approximate Bayesian computation in evolution and ecology. Ann Rev Ecol Evol Syst 41:379–406Google Scholar
- Bennett NC, Faulkes CG (2000) African mole-rats: ecology and eusociality. Cambridge University Press, CambridgeGoogle Scholar
- Bennett NC, Jarvis JUM, Cotterill FPD (1994) The colony structure and reproductive biology of the afrotropical Mashona mole-rat, Cryptomys darlingi. J Zool 234:477–487Google Scholar
- Burda H, Honeycutt RL, Begall S, Locker-Grütjen O, Scharff A (2000) Are naked and common mole-rats eusocial and if so, why? Behav Ecol Sociobiol 47:293–303Google Scholar
- Emlen ST (1982) The evolution of helping. I. An ecological constraints model. Am Nat 119:29–39Google Scholar
- Faulkes CG, Bennett NC (2013) Plasticity and constraints on social evolution in African mole-rats: ultimate and proximate factors. Philos. T. R. Soc. B. 368:20120347Google Scholar
- Felsenstein J (1985) Phylogenies and the comparative method. Am Nat 125:1–15Google Scholar
- Felsenstein J (2005) Using the quantitative genetic threshold model for inferences between and within species. Philos Trans R Soc B 360:1427–1434Google Scholar
- Garamszegi LZ (2014) Modern phylogenetic comparative methods and their application in evolutionary biology: concepts and practice. Springer, HeidelbergGoogle Scholar
- Hadfield JD (2015) Increasing the efficiency of MCMC for hierarchical phylogenetic models of categorical traits using reduced mixed models. Methods Ecol Evol 6(6):706–714Google Scholar
- Hadfield JD, Nakagawa S (2009) General quantitative methods for comparative biology: phylogenies, taxonomies and multi-trait models for continuous and categorical characters. J Evol Biol 23:494–508Google Scholar
- Harvey PH, Pagel MD (1991) The comparative method in evolutionary biology. Oxford University Press, OxfordGoogle Scholar
- Ives AR, Garland T (2014) Phylogenetic regression for binary dependent variables. In: Garamszegi LZ (ed) Modern phylogenetic comparative methods and their application in evolutionary biology: concepts and practice. Springer, Heidelberg, pp 231–261Google Scholar
- Janzen T, Hoehna S, Etienne RS (2015) Approximate Bayesian computation of diversification rates from molecular phylogenies: introducing a new efficient summary statistic, the nLTT. Methods Ecol Evol 6:566–575Google Scholar
- Jarvis JUM, Bennett NC (1993) Eusociality has evolved independently in two genera of bathyergid mole-rats—but occurs in no other subterranean mammal. Behav Ecol Sociobiol 33:253–260Google Scholar
- Jones K, Bielby J, Cardillo M, Fritz S (2009) PanTHERIA: a species-level database of life history, ecology, and geography of extant and recently extinct mammals. Ecology 90:2648Google Scholar
- Kutsukake N, Innan H (2014) Detecting phenotypic selection by approximate Bayesian computation (ABC) in phylogenetic comparative methods. In: Garamszegi LZ (ed) Modern phylogenetic comparative methods and their application in evolutionary biology: concepts and practice. Springer, Heidelberg, pp 409–424Google Scholar
- Marjoram P, Tavare S (2006) Modern computational approaches for analysing molecular genetic variation data. Nat Genet Rev 7:759–770Google Scholar
- Nunn CL (2011) The comparative approach in evolutionary anthropology and biology. University of Chicago Press, ChicagoGoogle Scholar
- Pagel M (1994) Detecting correlated evolution on phylogenies: a general method for the comparative analysis of discrete characters. Proc R Soc B 255:37–45Google Scholar
- R Core Team (2017) R: a language and environment for statistical computing. R Foundation for Statistical Computing, ViennaGoogle Scholar
- Sherman PW, Jarvis JUM, Alexander RD (1991) The biology of the naked mole-rat. Princeton University Press, PrincetonGoogle Scholar
- Sichilima AM, Faulkes CG, Bennett NC (2008) Field evidence for a seasonality of reproduction and colony size in the Afrotropical giant mole-rat Fukomys mechowii (Rodentia: Bathyergidae). Afr Zool 43:144–149Google Scholar
- Sichilima AM, Bennett NC, Faulkes CG, Bronner GN (2011) Field evidence for colony size and aseasonality of breeding and in Ansell’s mole-rat, Fukomys anselli (Rodentia: Bathyergidae). Afr Zool 46:334–339Google Scholar